Does It Count?

I saw an interesting question last night on Twitter (yes, I was lurking). They asked:
"If I run an ultra distance that's not part of a organized race, does it count?"

I have my own thoughts, but want to hear from you! If you run 26.2 miles or 36 miles or 50 miles that is not part of a race, does it count that you ran it? For example, can you say "I've run x marathons or x ultra marathons"? Or do they not "count"?